Interestingness as an Inductive Heuristic for Future Compression Progress

One of the bottlenecks on the way towards recursively self-improving systems is the challenge of interestingness: the ability to prospectively identify which tasks or data hold the potential for future progress. We formalize interestingness as an inductive heuristic for future compression progress and investigate its predictability using tools from Kolmogorov Complexity and Algorithmic Statistics. By analyzing complexity-runtime profiles under various priors over computable objects, we demonstrate that the inductive property of interestingness—the capacity for past compression progress to signal future discovery—is theoretically viable and empirically supported. Expected future progress depends crucially on the recency of the last observed progress. However, this dependency is highly sensitive to the underlying distribution of objects.